Plants modify nutrient availability by releasing chemicals in rhizosphere. This change in availability induced by roots (bioavailability) is known to improve nutrient uptake by individual plants releasing such compounds. Can this bioavailability alter plant competition for nutrients and under what conditions? To address these questions, we have developed a model of nutrient competition between plant species based on mechanistic descriptions of nutrient diffusion, plant exudation and plant uptake. The model was parametrized using data of the effects of root citrate exudation on phosphorus availability. We performed a sensitivity analysis for key parameters to test the generality of these effects. Our simulations suggest that: 1) Nutrient uptake depends on the number of roots when nutrients and exudates diffuse little, because individual roots are nearly independent in terms of nutrient supply. In this case, bioavailability profits only species with exudates. 2) Competition for nutrients depends on the spatial arrangement of roots when nutrients diffuse little, but exudates diffuse widely. 3) Competition for nutrients depends on the nutrient uptake capacity of roots when nutrients and exudates diffuse widely. In this case, bioavailability profits all species. Mechanisms controlling competition for bioavailable nutrients appear to be diverse and strongly depend on soil, nutrient and plant properties.